where \(\xi _{L}\)  is the linear correlation function and \(A_{ij}(q)\)  is the LPT displacement difference cumulant [1]}, [2]}, [3]}, [4]}, [5]}.
A benefit of taking \(P_{\mathrm {alt}}\)  as the starting point for a new two-halo term is that it remains easy to compute while preserving many of the advantages of ZA, and also provides slightly more power than ZA on quasi-linear scales.
This modified version of ZA can be further augmented in a manner similar to the models of [6]}, [4]} by adding a transfer function style polynomial term multiplying \(P_{\mathrm {alt}}\) , such that
\(P_{\mathrm {alt, HZPT}}(k) = \left(1 + \alpha k^{2} + \beta k^{4} \right)P_{\mathrm {alt}}(k) + P_{BB}(k)\) 
